Surface Acoustic Wave Coding for Orthogonal Frequency Coded Devices

ABSTRACT

Methods and systems for coding SAW OFC devices to mitigate code collisions in a wireless multi-tag system. Each device producing plural stepped frequencies as an OFC signal with a chip offset delay to increase code diversity. A method for assigning a different OCF to each device includes using a matrix based on the number of OFCs needed and the number chips per code, populating each matrix cell with OFC chip, and assigning the codes from the matrix to the devices. The asynchronous passive multi-tag system includes plural surface acoustic wave devices each producing a different OFC signal having the same number of chips and including a chip offset time delay, an algorithm for assigning OFCs to each device, and a transceiver to transmit an interrogation signal and receive OFC signals in response with minimal code collisions during transmission.

This application is a continuation-in-part of U.S. patent applicationSer. No. 11/508,674 filed on Aug. 23, 2006, now U.S. Pat. No. 7,623,037issued on Nov. 24, 2009, which claimed the benefit of priority to U.S.Provisional Patent Application No. 60/711,278 filed on Aug. 25, 2005 andU.S. patent application Ser. No. 11/521,708 filed on Sep. 15, 2006 whichclaimed the benefit of priority to U.S. Provisional Patent ApplicationNo. 60/718,575 filed on Sep. 19, 2005.

FIELD OF THE INVENTION

This invention relates to orthogonal frequency coding and surfaceacoustic wave devices and, in particular, to methods and systems forsurface acoustic wave coding for orthogonal frequency coded devices toreduce code collisions in a multi-tag system.

BACKGROUND AND PRIOR ART

The surface acoustic wave (SAW) sensor offers advantages in that it iswireless, passive, small and has varying embodiments for differentsensor applications. Surface acoustic wave (SAW) sensors are capable ofmeasuring physical, chemical and biological variables and have theability to operate in harsh environments. In addition, there are avariety of ways of encoding the sensed data information for retrieval.Single sensor systems can typically use a single carrier RF frequencyand a simple device embodiment, since tagging is not required. In amulti-sensor environment, it is necessary to both identify the sensor aswell as obtain the sensed information. The SAW sensor then becomes botha sensor and a tag and must transmit identification and sensorinformation simultaneously.

Known SAW devices include delay line and resonator-based oscillators,differential delay lines, and devices utilizing multiple reflectivestructures. Single sensor systems can typically use a single carrierfrequency and a simple coding technique, since tagging is not required.However, there are advantages of using spread spectrum techniques fordevice interrogation and coding, such as enhanced processing gain andgreater interrogation power.

The use of orthogonal frequencies for a wealth of communication andsignal processing applications is well known to those skilled in theart. Orthogonal frequencies are often used in an M-ary frequency shiftkeying (FSK) system. There is a required relationship between the local,or basis set, frequencies and their bandwidths which meets theorthogonality condition. If adjacent time chips have contiguous localstepped frequencies, then a stepped chirp response is obtained. See S.E. Carter and D. C. Malocha, “SAW device implementation of a weightedstepped chirp code signal for direct sequence spread spectrumcommunication systems”, IEEE Transactions on Ultrasonics,Ferroelectrics, and Frequency control, Vol. 47, July 2000, pp. 967-973.

Co-pending U.S. patent application Ser. No. 11/508,674 filed on Aug. 23,2006, assigned to the same assignee as the present application, teachesweighted surface acoustic wave reflector gratings for codingidentification tags and sensors to enable unique sensor operation andidentification for a multi-sensor environment. In an embodiment, theweighted reflectors are variable while in another embodiment thereflector gratings are apodized. The weighting technique allows thedesigner to decrease reflectively and allows for more chips to beimplemented in a device and, consequently, more coding diversity. As aresult, more tags and sensors can be implemented using a given bandwidthwhen compared with uniform reflectors. Use of weighted reflectorgratings with OFC makes various phase shifting schemes possible, such asin-phase and quadrature implementations of coded waveforms resulting inreduced device size and increased coding. The device may include asingle transducer/antenna pair with a bank of reflectors on one side ofthe transducer/antenna pair, or a bank of reflectors on both sides ofthe transducer/antenna pair, or alternatively, a unidirectionaltransducer may be used to reduce the device loss and size.

Co-pending U.S. patent application Ser. No. 11/521,708 filed on Sep. 15,2006, now U.S. Pat. No. 7,623,037 issued on Nov. 24, 2009, assigned tothe same assignee as the present application, and which is incorporatedherein by reference describes and claims a surface acoustic wave deviceincluding a substrate, at least two banks of reflectors fabricated onsaid substrate for producing at least two contiguous stepped frequenciesas an orthogonal coded signal, wherein each of said at least twocontiguous stepped frequencies have a different center frequency withina bandwidth and at least two transducer and antenna pairs each having adifferent tuned center frequency on said substrate, each of said atleast two transducer/antenna pairs coupled with one of said at least twobanks of reflectors for receiving an orthogonal frequency coded signalgenerated by a corresponding one of said at least two banks ofreflectors, wherein the bandwidth of each transducer/antenna pair isinversely proportional to the number of transducer/antennas pairs used.

Co-pending U.S. patent application Ser. No. 11/703,377 filed on Feb. 7,2007, assigned to the same assignee as the present application, which isincorporated herein by reference, teaches an orthogonal frequency codeddevice that includes a substrate, a transducer and plural acoustictracks each having a bank of reflectors fabricated on the substrate. Theplural acoustic tracks are coupled with the transducer and each acoustictrack produces a different code sequence with a different delay betweena starting chip sequence in each of the different code sequences. Thesum of the different code sequences forms an orthogonal coded signal forthe device to provide increased coding by including delays in the codesequences.

Each of the banks of reflectors includes a first and second bank ofreflectors located on opposite sides of said transducer and coupled withthe transducer. Each bank of reflectors includes plural reflectorscoupled together each producing an orthogonal frequency within abandwidth to generate the code sequence for a corresponding one of theplural tracks. A summation of the codes sequences from the plural tracksproduces the orthogonal coded signal for the device.

Surface acoustic wave tags, by their passive nature, are purely areflective device; changing amplitude, phase and/or delay of theinterrogation signal over the band of interest. Because of theseproperties, the SAW tag is equivalent to a radar target, with theexception that the return, or reflected signal, has been modified inamplitude, phase, or delay in a predefined manner. This change in deviceparameters is similar to the change of a radar target due to movementcausing a Doppler shift. Because there is no handshake in the wirelesspassive system, where device return signal parameters can be activelymodified, the return signals may return in overlapping time positionswith the desired signal energy, distorting the desired signal andpossibly causing false identification or parameter extraction. Since theOFC SAW devices are tagged using spread spectrum techniques foridentification, the device identification at the receiver isaccomplished using matched filter and correlation techniques, as well aspossibly digital signal processing. The device identification is madevia its code, and the overlap of other SAW tags/sensors in the range ofthe transmitter causes code collisions. Code collisions are a difficultproblem to mitigate given the asynchronous nature of the passive SAWtag. The co-inventors have researched numerous books and publications,with nothing of real value to aid in addressing the code collisionproblem for asynchronous, passive, multi-tag environments.

There are numerous publications and books on code auto- andcross-correlation properties. In an active communication system wherethere is a handshake between transmitter and receiver, the use of signallevel adjustment, orthogonal code sets, spatial diversity, andsynchronization can optimize a communication link. This active linkscenario provides many options to minimize code collision effects. Forthe SAW passive tag/sensor, the use of orthogonal code sets has littleto no value without the availability of transceiver synchronization andsignal level adjustment. Moreover, most work to date has been addressingCDMA codes and little effort on orthogonal frequency coding approaches.

For example, T-K Woo, Orthogonal code design for Quasi-synchronousCDMA”, Electronic Letters, September 2000, Vol. 36, #9, 1632 examinedorthogonal code design for quasi-synchronous CDMA. The last sentence inthe conclusion is, “However, the results for cross-correlation aremixed”. The Woo scheme has a lower variance but a higher mean”. Ingeneral, most analysis was done on a statistical basis for CDMA activesystems where it can be assumed that the signals are non-stationary. Inthe case of a fixed SAW device and a fixed interrogator, the signals arestationary and re-interrogating will just continuously give the wronganswer. Moreover, as code delays change with temperature or othermeasurand, the code collision can change from acceptable tounacceptable.

As another example, Dudzik, et. al., Orthogonal code design for passivewireless sensors, Communications, 2008 28^(th) Biennial Symposium on24-26 Jun. 2008, pp 316-319, describes orthogonal CDMA code design forpassive wireless sensors. Dudzik sets two criteria:

1. Largest peak-to-sidelobe ratio of the auto-correlation response of agiven code2. Smallest maximum peak value of cross-correlation of that code withany other code in the set.

Dudzik, et. al. shows only summary results and a SAW sensor application,but no useful details are given. But also important is the fact that thecriteria may not be correct in a passive, multi-sensor environment. Itappears that criteria (2) may be overly simplistic, since it is ourbelief that it is necessary to have the smallest maximum peak value ofcross-correlation of that code to the sum of all other codes in the setunder the interrogation range. This is a much more stringent anddifficult criteria.

Both examples are for CDMA coding and are not directly applicable toorthogonal frequency coding, but it does illustrate the lack ofavailable work on passive systems. The addition of the OFC-PN codinghelps the code collision problem, but does not eliminate basic energyconsiderations and physical limitations.

SUMMARY OF THE INVENTION

A primary objective of the invention is to provide methods, system,apparatus and devices for producing wireless, passive SAW sensors have avery small size and a cost of only a few cents each in quantities ofmillions.

A secondary objective of the invention is to provide methods, systems,apparatus and devices with multiple transducers and antennas for usewith orthogonal frequency coded SAW tags for temperature, pressure, gasand liquid sensors.

A third objective of the invention is to provide methods, systems,apparatus and devices for increasing the wireless sensor and tag rangeby reducing the device loss.

A fourth objective of the invention is to provide methods, systems,apparatus and devices for SAW sensors and tags using multipletransducer/antenna pairs each having a different center frequency toincrease bandwidth, further reduce device loss and improve overallperformance.

A fifth objective of the invention is to provide methods, systems,apparatus and devices that increases the bandwidth of a orthogonalfrequency coded SAW sensors and tags.

A first embodiment provides a method to mitigate code collisions in awireless multi-tag system, each one of the OFC surface acoustic wavedevices generating an orthogonal frequency coded signal foridentification. The method includes the steps of determining a M by Ncode matrix dimension based on the number of orthogonal frequency codesneeded M and the number of locations chips can populate N, each rowcorresponding to one surface acoustic wave device orthogonal frequencycode and each cell in each row corresponding to one orthogonal chip andthe chips are orthogonal to each other at their respective centerfrequencies, populating each cell of the matrix with one of theorthogonal frequency chips with a different one of the orthogonalfrequencies in each cell in each column, and applying one of theresulting codes from the populated matrix to each one of the surfaceacoustic wave OFC devices in the multi-tag system. The M by N matrixgenerating step includes determining the quantity of OFC surfaceacoustic devices M in the multi-tag system and determining the quantityof chips N in the orthogonal frequency coded signals for the OFC surfaceacoustic wave devices in the multi-tag system, wherein M is the numberof codes with one single code per SAW tag, the number of overlappingchips m includes same-frequency overlaps.

The overlap of the chips can be m=n, then N=M and the number ofoverlapping chips m excludes same-frequency overlaps. The matrix stepincludes retrieving each next available orthogonal frequency code andassigning each chip in the orthogonal frequency code a location in thematrix and can include setting an orthogonal frequency coding multi-tagsystem bandwidth having a system center frequency. The retrieving stepincludes retrieving the first orthogonal frequency code, retrieving thenext orthogonal frequency code when each chip in the first orthogonalfrequency code has been assigned a location in the matrix, determiningwhen the last chip in the last code has been assigned a location,returning the completed matrix when the last chip in the last code hasbeen assigned a location, and returning one of an error message and aninvalid code set when a location for one of the chips in the currentcode is not found.

The assigning step includes retrieving the each next chip in the firstorthogonal frequency code, assigning each next chip one of the cells inone row of the matrix, retrieving the next orthogonal frequency code,retrieving the next chip in the next orthogonal frequency code, locatingthe cells in a next row of the matrix that is not assigned one of thechip, locating the columns of the located cells that are not assignedthe same chip, locating the column with the least number of chips,assigning the chip to the cell in the column with the least number ofchips when a column is located, locating the column with the secondleast number of chips when the column with a least number of chips isnot located, assigning the chip to the cell in the column with thesecond least number of chips when the next column is located, returningthe one of the error message or the invalid code set when no next columnis located, determining if the chip is the last chip, repeating steps dthrough l when the chip is not the last chip, determining if the nextorthogonal frequency code is the last orthogonal frequency code,repeating steps c through n when the next orthogonal frequency code isnot the last orthogonal frequency code, and returning the completedmatrix when the last chip in the last code has been assigned a location.

A second embodiment provides an asynchronous passive multi-tag systemfor detecting each one of plural surface acoustic wave orthogonalfrequency coded devices in a multi-tag system. The system includes anorthogonal frequency coding system bandwidth having a system centerfrequency, plural surface acoustic wave devices each producing adifferent orthogonal frequency coded signal having the same number ofchips in the code, each of the different OFC signals including a chipoffset time delay, an algorithm for assigning an orthogonal frequencycoded identification to each of the plural devices, and a transceiver incommunication with the plural surface acoustic wave device fortransmitting an orthogonal interrogation signal to the plural surfaceacoustic wave devices and receiving the different orthogonal codedsignals from said plural surface acoustic wave devices. The chip offsetdelay can be a one chip offset delay between all of the pluralorthogonal frequency codes in the system or a two chip offset delaybetween all of the plural orthogonal frequency codes in the system. Thealgorithm includes a first set of instructions to determine a M by Ncode matrix dimension based on the number of orthogonal frequency codesneeded M and the number of locations chips can populate N, each rowcorresponding to one surface acoustic wave device orthogonal frequencycode and each cell in each row corresponding to one orthogonal chip andthe chips are orthogonal to each other at their respective centerfrequencies and a second set of instructions to populate each cell ofthe matrix with one of the orthogonal frequency chips with a differentone of the orthogonal frequencies in each cell in each column.

Further objects and advantages of this invention will be apparent fromthe following detailed description of preferred embodiments which areillustrated schematically in the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is an example of a stepped chirp response.

FIG. 2 is an example of an OFC chip frequency response.

FIG. 3 is an example of a 7 chip OFC waveform based on the placement ofchips.

FIG. 4 shows the time autocorrelation of a single carrier PN code and aPN-OFC signal having a 7 chip Barker code modulating the chips of bothsignals.

FIG. 5 shows the frequency response of a 7 chip PN-OFC signal and asingle carrier signal.

FIG. 6 is a graph showing the electromagnetic time delay verses range.

FIG. 7 is a plot showing the sum of all orthogonal frequency and pseudonoise codes as seen by the antenna.

FIG. 8 is a plot showing the superposition of the auto correlationpeaks, one at a time.

FIG. 9 is a plot showing the autocorrelation of a desired tag and thecross-correlation of the desired tag with the sum of the other tags.

FIG. 10 is a plot showing the sum of all tag responses at the antenna.

FIG. 11 shows the autocorrelations of the five shortest time-delay tags.

FIG. 12 is a plot showing the complete correlated signal of tag 16 willall of the other tag present.

FIG. 13 is a more detailed plot of the correlation region with onereference code.

FIG. 14 is a plot showing the sum of the ensemble tag response.

FIG. 15 is a plot showing the autocorrelations, one at a time.

FIG. 16 is a plot showing the complete signal autocorrelation of tag 16with one reference code.

FIG. 17 is a plot showing the complete signal correlated one referencecode

FIG. 18 is a flow diagram showing steps of the algorithm forsemi-randomly populating a matrix by produce codes using orthogonalfrequency coded chips.

FIG. 19 is a graph showing autocorrelation of the fifth code from Table7 compared with the correlation to the entire system.

FIG. 20 shows the correlation of code 5 to the entire system with code 5removed.

FIG. 21 a shows the best performing codes out of the 16 code set shownin Table 7.

FIG. 21 b shows the worst performing codes out of the 16 code set shownin Table 7.

FIG. 22 shows the autocorrelation of code 5 from Table 7 compared to theentire system, and the worst correlation out of 16 codes over a longertime period.

FIG. 23 a shows the overlap of the power spectra of adjacent chips (f₁adjacent to f₂).

FIG. 23 b shows the overlap of the power spectra of chips separated byone chip (f₁ and f₃).

FIG. 24 a shows the best performing codes out of the 16 code set shownin Table 9.

FIG. 24 b shows the worst performing codes out of the 16 code set shownin Table 9.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before explaining the disclosed embodiments of the present invention indetail it is to be understood that the invention is not limited in itsapplication to the details of the particular arrangements shown sincethe invention is capable of other embodiments. Also, the terminologyused herein is for the purpose of description and not of limitation.

It would be useful to review orthogonal frequency before discussing themethod, system apparatus and device for using orthogonal frequencycoding of the present invention. Orthogonal frequencies are used tospread the signal bandwidth. The orthogonality condition describes arelationship between the local chip frequencies and their bandwidths. Asan example, consider the stepped linear chirp shown in FIG. 1. Sevencoherent carriers are used to generate the signal shown. Each chipcontains an integer number of carrier half cycles due to theorthogonality condition. Under these conditions, the resulting waveformis continuous. The conditions, however, do not require that the localfrequency of adjacent chips, that are contiguous in time, be contiguousin frequency. Instead, the time function of a bit provides a level offrequency coding by allowing a shuffling of the chip frequencies intime.

The chip frequency response is shown in FIG. 2. These responses are aseries of sampling functions with null bandwidths equal to 2·τ⁻¹. Inaddition, the sampling function center frequencies are separated bymultiples of τ⁻¹. Coding is accomplished by shuffling the chips toproduce signal such as shown in FIG. 3, wherein the adjacent frequenciesare not required to be sequential. The code is now determined by theorder in which the orthogonal frequencies are used. Both signals occupythe same bandwidth and the coded information is contained within thesignal phase. A more complete description of orthogonal frequency codingis given in D. C. Malocha, et al., “Orthogonal frequency coding for SAWdevice application,” 2004 IEEE International Ultrasonics,Ferroelectrics, and Frequency Control 50^(th) Anniversary JointConference, in press, which is incorporated herein by reference.

In the example shown in FIG. 3, the seven local chip frequencies arecontiguous in frequency but are not ordered sequentially in time and thechip weights are all unity. If the local chip frequencies were orderedhigh to low or low to high, the time sequence would be a steppeddown-chirp and up-chirp, respectively. The start of the chip carrierfrequency begins at zero amplitude, as seen in FIGS. 2 and 3, which is acondition of the orthogonality.

The OFC technique provides a wide bandwidth spread spectrum signal withall the inherent advantages obtained from the time-bandwidth productincrease over the data bandwidth. The OFC concept allows for a widebandwidth, chirp interrogation, frequency and binary coding per bit, areduced compressed pulse width as compared to a PN sequence, and asecure code. The OFC technique of the present invention can be appliedto ultra-wide-band applications since the fractional bandwidth canexceed 20% and can be used in a multi-tag or sensor environment by usingproper coding techniques.

In addition to the OFC coding, each chip can be weighted as ±1, giving apseudo noise (PN) code in addition to the OFC, namely PN-OFC. This doesnot provide any additional processing gain since there is no increase inthe time bandwidth product, but does provide additional code diversityfor tagging. FIG. 6 shows the autocorrelation of a 7 bit Barker codeapplied to an OFC shown with a solid line and a single carrier frequencyshown with a dashed line. The pseudo noise code has a compressed pulsewidth of 2·τ_(C), or a PG_(PN)=7 as compared PG_(PN-OFC)=49. Thecompressed pulse width of the OFC is a function of the bandwidth spreadand not the pseudo noise code; yielding comparable pulse-width and sidelobes results, as shown in FIG. 4 with pseudo noise code.

FIG. 5 compares the waveforms of the frequency response of a 7-chipPN-OFC represented with a solid line and a single carrier pseudo noisesignal represented with a dashed line. As shown, each has approximatelythe same time lengths with the magnitudes normalized to the timeamplitude peak of the pseudo noise response. The PN-OFC has an increasedprocessing gain and a narrower compressed pulse peak over just thepseudo noise sequence, proportional to the bandwidth spreading of theOFC.

For the purpose of the following analysis, the OFC design is similar tothe OFC design principles described in co-pending patent applicationSer. Nos. 11/508,674 filed on Aug. 23, 2006, 11/521,708 filed on Sep.15, 2006 and 11/703,377 filed on Feb. 16, 2007 each having the sameassignee as the subject application and having a common inventor whichare incorporated herein by reference. The orthogonal frequency codeddevice center frequency is assumed at approximately 250 MHz. The chipreflector for device discussion has 25 electrodes at 250 MHz whichyields a chip time length of approximately 100 nsec. The chip timelength maintains a near Rect function in time and Sampling (Sa) functionin the frequency domain when implemented on the surface acoustic wavedevice. The actual SAW velocity is modified, depending on the metalpattern of the surface, as the surface acoustic wave propagates fromtransducer to the reflector and back.

For the following analysis and calculation the free surface SAW velocityis assumed at 3488 m/sec. The chip null bandwidth is 20 MHz and the chipbandwidth is approximately 10 MHz. These numbers are typical of theco-pending patent application, but are not critical. The code analysisassumes that the ideal chips are good approximations to the SAW chips.This has been verified experimentally for chip reflector lengths lessthan approximately 50 electrodes on YZ LiNbO₃. The chip lengths arevariable, dependent on many device and system parameters. The followingcode analysis plots are scaled to chip lengths to provide a nearuniversal analysis. As chip lengths, bandwidths, center frequencies,etc. vary, the code simulations are still valid with proper scaling.

For purpose of discussion the operating temperature range is assumed as30° C.+/−50° C. which yields a 100° C. temperature range. For YZ LiNbO₃,the temperature coefficient of delay (TCD) is approximately 96 ppm/° C.over the temperature range, with a total temperature coefficient ofdelay change of approximately 9600 ppm. At 250 MHz, this translates to amaximum frequency shift of approximately 250×9600=2.4 MHz, or +/−1.2 MHzfrom the nominal center frequency over the temperature limits.

For this analysis, the range is limited to approximately 5 meters with avariation of +/−1 meter. The round trip electromagnetic delay time at 5meters is approximately 34 nsec and a one meter variation yields a 6.8nsec tie variance. The nominal range is not important for coding but isimportant for system range because it changes the received target signalpower variation and also changes the delay at the receiver. For thecurrent analysis, it is assumed that the range of the tags is identical.

The SAW tag, matching and antenna response is a function of severalcomponents. All of these components compose the sensor target. Thecomplete impulse frequency response of the target is given by theproduct of the transfer functions as

${H_{Target}(f)} = {\begin{pmatrix}{{H_{Antenna}(f)} \cdot {H_{Matching}(f)} \cdot} \\{{H_{SAW\_ prop}(f)} \cdot ^{{- ^{\omega}}{TD}} \cdot {H_{Transducer}(f)}}\end{pmatrix}^{2} \cdot {H_{Reflector}(f)}}$

where τ_(D) corresponds to the delay between the transducer and thereflector. If it is assumed that the antenna and matching circuits arebroadband and have no significant effect on the target transferfunction, then the three component transfer functions of interest in thedesign are the propagation delay, the transducer and the reflector. Thetotal transfer function of interest is given by

H _(Total)(f)=(H _(prop)(f)·e ^(jωτD) ·H _(Transducer)(f))² ·H_(Reflector)(f)

In general, the reflector and transducer can both be coded and the delaywithin the transducer and reflector, modifying both chip and bitsequences, can vary. This report assumes the transducer has an idealfrequency response of unity over the bandwidth of interest.

For the SAW, passive wireless sensor scenario, it is assumed that anumber, N_(sensor), of devices are responding to the interrogationsignal at some minimum energy level. Over a measurement interval, thedevice outputs are assumed stationary in time. It is assumed that eachtag has the same device parameters, except for the actual device code,and that each re-transmitted signal is at the same level. Therefore,once activated by the interrogation signal, each tag can be consideredas a mini-transmitter having a given signal format and level.

At the receiver, each sensor signal is summed at the antenna yielding asingle input signal to the receiver. The consequence of this summing atthe antenna input is that all overlapping chips in time, from the sum ofall sensors, are no longer distinguishable from each other. If the chipswere all synchronous in time and all had the same chip carrierfrequency, then the sum would be a random chip signal having a widerange of amplitudes and whose phase could be arbitrarily 1 or −1.

As a simple example, if a CDMA code set is assumed having only twocodes, and if the two codes at an overlapping chip interval were +1 and−1, respectively, then the signal energy present at the antenna is zero.If the signal amplitudes are the same, then the sum is 2, again thewrong answer for the desired signal chip. This results in a completeloss of chip information over this interval. When correlating againstthis chip, the result is completely ambiguous. With one chip in asequence this would not be a grave problem, but if many chips areoverlapping from many sensors the correlation signal is soon lost. Givena large number of chips and sensors, the results can either be simulatedor statistically determined, but doing a complete code set analysis areimpossible within reasonable and given time constraints.

With an orthogonal frequency code set, the problem of chip overlap isreduced since there is both frequency and PN code diversity. Chipsoverlapping from two sensors are generally at different orthogonalfrequencies and the signal energy information should be maintained,unless the two sensors have the same chip frequency in the timeinterval.

The co-inventors have been researching different approaches to amulti-tag/sensor system; most of which do not allow plural tags to beinterrogated at one time. Approaches to just coding algorithms has beenmarginally fruitful. Over the course of the research it was concludedthat the previous energy arguments provide a physical barrier, withexpected limits. Given the complexity of coding, sum of codes, and auto-and cross-correlation effects, the multi-parameter space seems extremelylarge and intractable. It is accepted that the energy limitation as theprime parameter for a multi-sensor, passive coded tag design and havefocused on means for overcoming the energy barrier, at least over somespecifications.

The co-inventors have previously published results showing that thecross correlation between differing OFC frequency chips yield lowercorrelation sidelobes, this is an important plus over normal CDMA. Theuse of both frequency division (FD) between tags and time division (TD)of chips in tags were also discussed. Both of these approaches wereconsidered since each provides greater diversity of coding in amulti-sensor system. Both approaches also provide some measure oforthogonality, based on implementation technique, over and above that ofjust orthogonal frequency coding. Experiments have shown that thepresent invention works for at least 32 tags, for example and notlimitation. The analysis assumed all tags of equal signal strength,having a known position, and all at the same absolute range. This is theinitial scenario at which the tags must be identifiable. The approachuses what the co-inventor call block-TD (BTD) coding of the multi-tagcode system.

To discuss the key points in consideration, a 5 chip, 32 tag,multi-sensor system is assumed for purpose of the example. The firstcase shows the results of the 32 tags having differing randomlygenerated OFC-PN codes without bit transmission delay (BTD) applied. Alltags are assumed to have identical delay offsets (approximately 4.5chips for the case below and is arbitrary). The tags each have 5 OFCchips starting at the same relative time and having the same exactlengths, however, the PN sequence and OFC sequence vary. The plot shownin FIG. 7 is the sum of all codes as seen at the antenna. The time delayoffset is completely arbitrary and was set for convenience of plotting.The signal length is 5 chips since all codes arrive simultaneously intime at the antenna. The signal looks like noise, as expected, over theexpected time duration.

The plot shown in FIG. 8 is the superposition of the 5 correlationpeaks, again all occurring at the same time as expected. The peaks fallonto each other and the sidelobes are slightly different, but not ofinterest. The time length is 5 chips, as expected.

The plot shown in FIG. 9 is the autocorrelation of a desired tag (boldline), and the cross correlation of the desired tag with the sum of allother tags (dashed line). As is evident, there is no discernableautocorrelation peak and it is clearly below the cross-correlation“noise”. This is a simple demonstration of the problem to be solved.

Our conclusion is that there must be time diversity, in addition to theOFC diversity, in the system. The problem is that the cross-correlationis stationary over a range of measurement cycles, but unpredictable.Therefore, a way to reduce the cross-correlation “noise” due tomulti-codes is to reduce the number of tags, eliminate thecross-correlation effect one tag at a time, and/or spreading the systemtag energy in time. The following description focuses on spreading thesystem tag energy in time.

For bit transmission delay, the total number of tags is treated as acomplete system and then the system is optimized as a whole. The mostcritical issue is the minimization of the cross-correlation noise andnot be overly concerned about the auto-correlation characteristics, atleast to first order. The realization is that the cross-correlationnoise is the primary factor limiting the number of OFC tags in a passivewireless multi-sensor system and optimization of a single or a fewchannels does not result in a good overall system.

For this bit transmission delay example, each OFC-PN code is offset by 1chip length in time. This has the effect of reducing code collisions forthe ensemble, but lengthens the overall system time length, as shown inFIG. 10. The system time length is now 36 chips long. The time delayoffset is arbitrary, but for this example, the idealized device timelength is approximately 10 chips long in time, the last device is 43chips long, with the last 5 chips having the code and the rest ispropagation delay. The time diversity spreads the tags ensemble energyin time, thereby reducing the time energy density. This is accomplished,however, at the expense of longer delays in devices, which translates tolonger SAW devices.

The sum of all tag responses at the antenna is shown in the plot of FIG.10. Similar to the case before, the time response appears as noise,however, the time response is longer than the previous case, asexpected. The autocorrelations of the five shortest time-delay tags areshown in FIG. 11. As expected, the autocorrelations no longer overlay intime, but are separated by 1 chip time length. The time delay offseteffectively moves the peak autocorrelation into a time bin approximately1 chip wide. This time domain orthogonality allows unambiguous detectionif the cross-correlation noise is at an acceptable level, so long as theautocorrelation peak does not move outside its time bin due toenvironmental changes or large changes in range.

The plot shown in FIG. 12 is the complete correlated signal of tag 16,with all other tags present. The ideal predicted auto-correlation(bold-line) highlights the expected height and position of the desiredresponse and the ensemble response (dashed-line) has a correlation peakat the desired position. It is noteworthy that if the position of thedesired correlation were unknown, it would not be possible to discernwhich time peaks to choose. The time orthogonality of the BTDM systemallows proper detection of the desired signal.

A more detailed plot of the correlation region is shown in FIG. 13. Thepeak pulse is as expected, although the cross-correlation peaks arenearly as large which may not be desirable. However, compared to theprevious example, the correlation is certainly discernable.

The last example is where a two chip offset BTD, having the same otherparameters as previously discussed, was considered. The sum of theensemble tag response is shown in FIG. 14. Note that there are quitezones where the sum of all chips is zero due to energy summing to zerofrom the chip ensemble, as a possibility previously discussed. Theensemble time length is now 67 chips long.

The autocorrelations of the first five chips shown in FIG. 15 arefurther separated when compared to the previous example. Theautocorrelation (bold line) and correlation of tag 16 with the ensemble(dashed line) are shown in FIGS. 16 and 17. The predicted correlationlooks good; the difference in amplitude is due to the chip interactionsreducing the energy of the correlation process.

In summary, the previous examples show that a 32 tag system, with 5 OFCchips, using a 2 chip delay TD OFC-PN sequence works well at roomtemperature. The distance between tags should allow operation over atleast 100° C. changes in temperature and at least +/1 range deviation.

On a YZ LiNbO₃ substrate, assuming a 100 nsec chip length, the longestcode plus offset delay distance is approximately 28 mm. Based on thiscurrent analysis, it is recommended that at least a 2 chip offset beused since it gives little autocorrelation pulse distortion and hasreduced time energy density.

The previous examples showed the results of a 5 chip TDD scheme. It isobvious that this can be extended to any number of chips. Also, althoughthe chips were placed in time slots, such that all OFC chips in a givendevice are contiguous in time, this is not necessary. The TDD scheme canbe extended so that the chips have time slots where there is no energybetween chips. Based on the previous arguments, it is only necessarythat the autocorrelation peaks are separated by an acceptable designdifference in time. It is also obvious that this can be extended to POFCor other similar frequency diverse coding structure. This technique canbe extended by using FDD techniques, such as band-limiting sets of tagswith respect to others, removing one or more adjacent OFC chipfrequencies, etc.

The following calculates the total ideal impulse response length of ageneral TDD system with a given time offset.

Define:

τ_(c)=chip time lengthτ_(offset)=offset time delayτ_(system)=system time length for all coded RFID devices

N_(C)=number of chips in code

N_(codes)=number of RFID codes devices in the system

f_(o)=system center frequency

BW=chip bandwidth

BW_(sys)=total OFC system bandwidth (BW_(sys)=N_(C)·BW_(c))

% BW=BW_(sys)/f_(o)

The total system ideal time length for all RFID devices is given as

τ_(system) = τ_(c) ⋅ [N_(c) + (τ_(offset)/τ_(c)) ⋅ (N_(codes) − 1)] orτ_(system) = 1/BW_(sys) ⋅ [N_(c)² + (τ_(offset)/τ_(c)) ⋅ (N_(codes) − 1)]

As an example, if the number of OFC chip frequencies is 5 and they arecontiguous within a block of time, there are 32 codes, and there is atime offset of 2-chip lengths, then the system ideal time length is

τ_(system)=τ_(c)·[5+2·(32−1)]=67·_(c)

There are many variations of the TDD approach to surface acoustic wavecoding. The following are examples provided to illustrate differentapproaches although the examples are not exhaustive, they do show someof the properties of different TDD approaches.

The vehicle chosen for the example is a 5-chip OFC with 8 codes in thesystem. A device chip sequence is given in each row, and the firstcolumn represents the beginning of the device with the shortestimplemented delay. Tables are used for the illustrations. Each arrayelement in the table is assumed to be a chip length in time. The chipsare numbered 1 through 5 and represent place holders; not any particularOFC frequency or phase. The delay offsets are in units of an integerchip length since it makes the illustrations easy to view, but from theabove calculations they are not required to be an integer chip length.

There are several competing considerations: 1) minimize code collisionsand the sum of all energy at any given time from all codes, 2) be ableto detect the auto-correlation peak without error under all systemoperational conditions, and 3) keep device lengths short or at leastrealizable for implementation in the SAW device embodiment. These aregenerally competing requirements where optimizing one will tend toexasperate the other. All the examples show the thermal equilibriumcondition which is ideal.

The first example shown in table 1 below is a system without time delayoffset.

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 12 3 4 5All of the codes have the same minimum delay which aligns all of thechips in each column, producing a code sum of 8 for all time chip slots.In fact, as the number of codes increases, the code sum in all columnsis always equal to the number of codes present, which optimizes codeoverlap and code collisions. The autocorrelations lies at the same pointin time. In general, this is a worst case scenario unless the number ofcodes is small. In general, code diversity does not provide enoughprocessing gain to overcome the cross-correlation energy of the sum ofall codes with the desired code. However, the time response of theentire system is only 5 chips long, making all devices small and thesystem time window of interest (TWI) small.

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 12 3 4 5Table 2 corresponds to the second example 2. In this example, each codehas been offset by a minimum of 1 chip length with respect to all othercodes. As shown, the first code has no offset, the second code has a onechip length offset, the third code has a two chip length offset, and soon. The sum of all codes within any column is always less than or equalto 5, which is true regardless of the number of codes. This can be anenormous decrease in code collisions and code overlap as the number ofsystem codes increases. The autocorrelation of each code occurs in aunique time slot with the next nearest autocorrelation being 1 chipaway. This should make signal detection easier and more accurate. Thedisadvantage of this approach compared to the first example is that thesystem time window of interest is longer and the length of the longestdevice is 7 chips more than the shortest device.

The table for example 3 is shown below.

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 12 3 4 5Here, each code has been offset by a minimum of 2 chip lengths withrespect to all other codes. The sum of all codes within any column isalways less than or equal to 3, and is true regardless of the number ofcodes. Similar to example 2, this is an enormous decrease in codecollisions and code overlap as the number of system codes increases. Theautocorrelation of each code occurs in a unique time slot with the nextnearest autocorrelation being 2 chips away. Again, this should makesignal detection easier and more accurate compared to example 1 and 2.The disadvantage of this approach compared to example 2 is the systemtime window of interest is again longer and the length of the longestdevice is 14 chips more than the shortest device.

The table for example 4 is shown below. In example 4 there is no chipdelay offset, 5 chip OFC, 9 chip code, zero coding is allowed.

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 12 3 4 5Here, each code has been offset by a minimum of 1 chip length withrespect to all other codes. However, the OFC chips are not contiguous intime. The example shows a zero weight time slot between non-zero weightcodes. This is just one of many cases where zeros can be included. Thesum of all codes within any column is always less than or equal to 4,and is always true regardless of the number of codes. The calculation ofsystem time length is similar to previous cases, with the exception thatthe code chip length is now 9 instead of 5, even though there are only 5OFC chips. Similar to example 3, this is a substantial decrease in codecollisions and code overlap as the number of system codes increases. Theautocorrelation of each code occurs in a unique time slot with the nextnearest autocorrelation being 1 chip away. Again, this should makesignal detection easier and more accurate compared to example 1. Thedisadvantage of this approach is the system time window of interest is16 chips compared to 12 chips for example 2, but is shorter than example3 which has a TWI of 19 chips.

Example 5 is a semi-chip delay offset, 5 chip OFC, 9 chip code, withzero coding allowed. The table for example 5 is shown below.

1 2 3 4 5 1 2 3 4 5 5 1 2 3 4 5 1 2 3 4 5 4 1 2 3 5 4 1 2 3 5 4 3 1 2 54 3 1 2In the previous examples, the code was offset by 1 chip length withrespect to the shortest code delay and the OFC chips are not contiguousin time. The fifth example shows a zero weight time slot betweennon-zero weight codes, as in example 4. The sum of all codes within anycolumn is always less than or equal to 4, and is dependent on the numberof codes. The calculation of system time length differs from previousexamples in that the code chip length is now 9 instead of 5, even thoughthere are only 5 OFC chips, and the time window of interest is only 10chips long. There are a maximum of 4 chip overlaps in any column (timeslot) for this case of 8 codes, but this number increases as the numberof codes increases. The acceptable levels of code energy in any timeslot must be considered for the system. The autocorrelation of each codeoccurs in the same time slot which means code diversity is crucial foraccurate, error-free detection. An advantage is that with this 8 codeset, every device has the same length and the overall system length isonly 10 chips; only twice as long as example 1.

The next example illustrates the use of code redundancy. Given theprevious examples, it is possible in many cases to reuse codes when TDDis implemented. The table below shows the case where there are 4different codes which are each reused twice.

1 2 3 4 5 5 4 3 2 1 2 4 1 3 5 5 3 4 2 1 1 2 3 4 5 5 4 3 2 1 2 4 1 3 5 53 4 2 1The autocorrelation peak of the first and fifth codes occurs in slots 3and 7, respectively. These are well separated in time and therefore donot interfere. The use of optimized code sets is simplified since anoptimized set can be reused. An important advantage to such a scheme isthat multiple tags can be auto-correlated at one time which can reduceprocessing complexity and time at the receiver. This approach can beused in conjunction with many of the previous examples.

The present invention introduces cell-based coding for OFC devices. Theidea of this approach is to take a set of OFC devices and spread chipsin time in such way that the same frequency chips have minimal number ofsame frequency overlaps in a given time slot. This can be represented asa matrix M×N, where N is number of locations where chips can be, and Mis number of codes needed. If we have n chips per OFC device and wedesire to have m overlapping chips (with or without same-frequencyoverlaps), N can be expressed as M, n and m, as shown in Eq. (1).

$\begin{matrix}{N = {{ceil}\left( \frac{n \cdot M}{m} \right)}} & (1)\end{matrix}$

In case of OFC devices all of the chips are orthogonal to each other attheir respective center frequencies; therefore, the most efficient wayto overlap the chips is when m=n, then N=M.

When populating this M×N matrix with OFC chips, it is important to keepin mind that each one of the frequencies can only be used once percolumn. Each chip is typically used once for every OFC device. Thealgorithm for populating such a matrix with codes is shown in FIG. 18.As shown, the instructions start with determining the code matrixdimensions of the code matrix M×N in step 110. As previously described,the code matrix is determined by the number of OFC devices M in themulti-tag system, number of locations N chips can populate, number ofchips n per OFC device, and the number of overlapping chips m allowed.

Once the dimensions of the matrix are determined, the matrix ispopulated. In steps 112 and 114, respectively, the first code and firstchip in the code is retrieved the cells of the current code that are notassigned a chip are determined in step 116. Based on the cells locatedin step 116, the columns corresponding the located cells are searched instep 118 to locate columns do not already contain the same chip. Oncethe columns are located, it is determined in step 120 which column isalready populated with the least number of chips. If a cell is found instep 122, the cell is populated with the chip in step 130. If a cell isnot located in step 122, the columns are searched to find the columnwith the second smallest number of chips is determined in step 124. Instep 126 it is determined if a column was found, and if a column islocated the cell is populated in step 130. In the event that a column isnot located in step 126, an error message is generated in step 128.

After a cell is populated with the chip in step 130, it is determined instep 132 if it was the last chip in the code. If it was the last chip,in step 140 it is determined if it is the last code in the code set. Ifit was the last code in the code set, then the process is complete andthe resulting populated matrix is returned in step 144. If it is not thelast code in the code set, the next code is found in step 150 and thefirst chip found in step 114, repeating the steps until an error occursor the matrix cells are fully populated.

During experiments, the algorithm was run many times and never returnedan error message or an invalid code set. Thus, it seems that a validsolution is produced at all times. In an event when algorithm returns aninvalid code set or an error, it can be re-run until it produces adesired outcome.

An example of 16 codes is shown in the next Table 7.

0 0 7 5 3 0 0 0 6 0 0 2 0 1 0 4 4 5 0 0 0 2 6 7 0 1 3 0 0 0 0 0 5 4 3 60 0 0 0 0 0 7 0 1 0 2 0 0 0 0 0 5 0 1 3 0 2 0 0 6 4 0 7 0 0 0 0 0 3 0 52 7 0 1 0 6 4 0 7 0 4 3 1 6 2 0 0 0 0 0 0 0 5 0 0 6 0 0 0 7 0 0 1 0 5 34 0 0 2 2 7 1 0 6 0 3 0 0 0 0 4 0 5 0 0 0 0 0 0 0 0 0 4 3 5 6 0 2 0 7 10 0 0 1 2 5 7 0 0 4 0 6 0 0 3 0 0 3 6 2 0 0 0 1 0 0 4 0 5 7 0 0 1 0 0 07 0 5 0 4 0 0 0 0 2 6 3 0 0 2 4 0 1 0 0 5 0 0 7 3 0 0 6 6 1 5 7 0 0 4 00 3 2 0 0 0 0 0 3 0 0 0 4 0 0 2 0 6 0 0 7 0 1 5 0 2 0 0 0 4 0 6 7 0 1 50 3 0 0It can be seen in highlighted row 7 and column 8 that each frequency isonly used once in each column. Also note that PN coding on top of OFCcoding has not yet been applied. FIG. 19 shows the correlation withaverage performance found of all 16 codes and the autocorrelation ofcode 5 from the above table compared to correlation to entire system,average performing correlation out of 16 codes.

FIG. 20 shows correlation of code 5 to entire system with code 5 removedfrom it. The most important thing to note is that the cross-correlationside lobes shown in FIG. 20 are small, and will remain small if anycodes are removed or attenuated.

FIGS. 21 a and 21 b show the best (a) and the worst (b) performing codesout of the 16 code set. Since any one of the frequencies is present inany one of the columns, when the sliding correlator (matched filter) isapplied as it is shifted by a chip length, there are always chips thatit will correlate. The worst case is when all of the chips are in phase;the result will be peaks at every chip length. This effect is shown inFIG. 22. Although the other correlations could be large, as long as thewindow of interest is smaller, as in FIG. 22, the code detection isaccurate. FIG. 22 shows autocorrelation of code 5 from Table 7 comparedto correlation to entire system, the worst correlation out of 16 codesover longer time period.

For a sensor, if the peaks start to overlap due to temperature,significant code collision can result. However, based on priorexperiments, to even shift by half of a chip length, extremetemperatures are required for most SAW substrates. Table 8 is anillustration of how these false correlations appear.

0 6 0 0 0 7 0 0 1 0 5 3 4 0 0 2 0 6 0 0 0 7 0 0 1 0 5 3 4 0 0 2 0 6 0 00 7 0 0 1 0 5 3 4 0 0 2 0 0 7 5 3 0 0 0 6 0 0 2 0 1 0 4 4 5 0 0 0 2 6 70 1 3 0 0 0 0 0 5 4 3 6 0 0 0 0 0 0 7 0 1 0 2 0 0 0 0 0 5 0 1 3 0 2 0 06 4 0 7 0 0 0 0 0 3 0 5 2 7 0 1 0 6 4 0 7 0 4 3 1 6 2 0 0 0 0 0 0 0 5 00 6 0 0 0 7 0 0 1 0 5 3 4 0 0 2 2 7 1 0 6 0 3 0 0 0 0 4 0 5 0 0 0 0 0 00 0 0 4 3 5 6 0 2 0 7 1 0 0 0 1 2 5 7 0 0 4 0 6 0 0 3 0 0 3 6 2 0 0 0 10 0 4 0 5 7 0 0 1 0 0 0 7 0 5 0 4 0 0 0 0 2 6 3 0 0 2 4 0 1 0 0 5 0 0 73 0 0 6 6 1 5 7 0 0 4 0 0 3 2 0 0 0 0 0 3 0 0 0 4 0 0 2 0 6 0 0 7 0 1 50 2 0 0 0 4 0 6 7 0 1 5 0 3 0 0The green highlighted column (row 2; row 10 columns 2, 7, 9 11-13 and16) represents the code at equilibrium (ideal). In Table 8, when thecode is shifted to the left (row 1, row 11 column 12, row 12, column 10,row 14 column 8, row 15 column 5 and row 17 column 1), each chip of thecode aligned with the same frequency chip from one of the other devices.When the code was shifted to the right, the chip with frequency 2 wasmoved outside of the matrix (row 3); therefore, the false peak at thatlocation is going to be 6/7 of the main correlation peak, given thatreflected wave amplitude is equal for all devices in the system. Thiscan also be observed in FIG. 22, where false correlation peaks decreasein steps of 1/7 when normalized to the main correlation peak.

In regard to frequency diversity of coding OFC Chip, for the generalcontiguous OFC coding, there is a frequency overlap of between adjacentchips, as shown in FIG. 23. In the case of 7 chip OFC devices, there are7 frequencies. To reduce the overlap of the power spectra of chips, ineach column only non-adjacent chip frequencies are used. As an example,for the 7-chip OFC codes the best that can be done is when four 4frequencies f₁, f₃, f₅, and f₇ are used. If four 4 overlaps are allowed,from Eq. 1 28 even columns (N) would be needed. The obvious solution tothis problem is to create two sets of codes; one that uses only oddfrequencies and one that uses only even frequencies. In the first subsetm=n=4 and in the second subset m=n=3, for 16 codes two matrices areproduced, both matrices are 16×16. When combined, each code becomes 32cells long, compared to 28 calculated earlier, this sounds reasonable.The table below shows the new code set that has these properties.

0 6 0 0 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 6 0 0 0 0 0 4 0 0 0 2 0 0 0 00 3 0 0 0 0 2 0 0 4 0 0 0 0 0 0 0 6 0 0 0 4 0 0 0 0 0 0 0 0 0 6 2 0 0 00 0 3 0 0 0 0 0 0 4 6 0 0 2 0 0 0 0 0 0 0 0 7 0 0 0 2 0 0 0 0 0 4 0 0 00 6 0 0 0 0 0 0 0 0 0 0 0 0 6 0 2 0 0 0 0 4 0 0 0 2 0 0 0 0 0 0 0 0 0 00 4 6 0 0 0 1 0 0 0 0 0 4 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 0 6 0 0 00 0 0 0 0 0 0 0 0 0 0 2 0 6 0 0 0 0 0 0 0 4 0 0 0 0 0 5 0 0 4 0 0 0 2 00 0 0 0 0 6 0 0 0 0 7 0 0 0 0 0 0 0 4 0 0 0 0 6 0 0 2 0 0 0 1 0 0 0 0 60 0 2 0 0 4 0 0 0 0 0 0 0 5 6 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 0 0 0 0 0 40 0 0 0 0 2 6 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 7 0 1 3 0 0 0 5 0 0 0 0 71 0 0 0 0 0 0 0 0 0 7 3 0 0 0 0 5 0 0 0 0 1 0 0 0 0 7 0 0 0 0 0 0 5 1 00 0 0 0 0 5 0 0 0 0 1 0 0 3 1 7 0 0 3 0 0 0 0 5 0 0 0 0 0 0 0 7 0 0 3 01 0 0 0 5 0 0 0 3 0 0 0 0 5 0 0 0 7 0 0 0 0 1 0 0 0 5 0 0 7 0 3 0 0 0 30 0 0 0 0 1 0 0 5 0 7 0 7 0 0 1 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 00 0 0 5 0 0 5 0 0 0 0 3 7 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 7 0 3 0 0 0 0 50 1 0 0 0 3 0 0 0 7 3 0 0 0 5 0 7 0 0 0 0 1 0 0As shown, the table includes codes for sixteen 16 devices with odd andeven frequencies separated. The table also includes an additional columnof zeros (highlighted) was added to further separate the chips from thetwo subsets. FIG. 24 shows the best and the worst performing codes outof the set in the above table showing the combined matrices.

FIGS. 24 a and 24 b show the best (a) and the worst (b) performing codesout of the 16 code set. When the worst and the best case of codes fromtable 9 above are compared to best performing codes of Table 1 shown inFIGS. 21 a and 21 b respectively, this method shows an advantage. Onaverage, codes from last set perform as good as the best code from thefirst table corresponding to the first example.

Up to this point PN coding was not used. Use of PN coding reduces codecollision (ripple around main correlation peak) even further and reducesfalse correlation peaks. The best that can be done with falsecorrelation peaks with 7 OFC chips is making them one-seventh 1/7 heightof main correlation peak. Theoretically, it could be reduced to zerowith an even number of chips; however, such a code set would heavilydepend on not only presence of every code, but also on amplitudes ofreflected waves, which should be very similar for every device.

While the invention has been described, disclosed, illustrated and shownin various terms of certain embodiments or modifications which it haspresumed in practice, the scope of the invention is not intended to be,nor should it be deemed to be, limited thereby and such othermodifications or embodiments as may be suggested by the teachings hereinare particularly reserved especially as they fall within the breadth andscope of the claims here appended.

1. A method to mitigate code collisions in a wireless multi-tag system,each one of the OFC surface acoustic wave devices generating anorthogonal frequency coded signal for identification, the methodcomprising the steps of: determining a M by N code matrix dimensionbased on the number of orthogonal frequency codes needed M and thenumber of locations chips can populate N, each row corresponding to onesurface acoustic wave device orthogonal frequency code and each cell ineach row corresponding to one orthogonal chip and the chips areorthogonal to each other at their respective center frequencies;populating each cell of the matrix with one of the orthogonal frequencychips with a different one of the orthogonal frequencies in each cell ineach column; and applying one of the resulting codes from the populatedmatrix to each one of the surface acoustic wave OFC devices in themulti-tag system.
 2. The method of claim 1 wherein the M by N matrixgenerating step comprises the step of: determining the quantity of OFCsurface acoustic devices M in the multi-tag system; and determining thequantity of chips N in the orthogonal frequency coded signals for theOFC surface acoustic wave devices in the multi-tag system, wherein M isthe number of codes with one single code per SAW tag.
 3. The method ofclaim 1 wherein the matrix determination step comprises the steps of:setting n as the number of chips per OFC device; setting m as the numberof overlapping chips allowed in the matrix; and determining a M by Ncode matrix dimension according to$N = {{ceil}\left( \frac{n \cdot M}{m} \right)}$
 4. The method of claim3 wherein the number of overlapping chips m includes same-frequencyoverlaps.
 5. The method of claim 4 wherein overlap of the chips isselected as m=n, then N=M.
 6. The method of claim 3 wherein the numberof overlapping chips m excludes same-frequency overlaps.
 7. The methodof claim 1 wherein the populating the matrix step comprises the step of:retrieving each next available orthogonal frequency code; and assigningeach chip in the orthogonal frequency code a location in the matrix. 8.The method of claim 1 wherein the retrieving step comprises the stepsof: retrieving the first orthogonal frequency code; retrieving the nextorthogonal frequency code when each chip in the first orthogonalfrequency code has been assigned a location in the matrix; determiningwhen the last chip in the last code has been assigned a location;returning the completed matrix when the last chip in the last code hasbeen assigned a location; and returning one of an error message and aninvalid code set when a location for one of the chips in the currentcode is not found.
 9. The method of claim 8 wherein the assigning stepcomprises the steps of: a) retrieving the each next chip in the firstorthogonal frequency code; b) assigning each next chip one of the cellsin one row of the matrix; c) retrieving the next orthogonal frequencycode; d) retrieving the next chip in the next orthogonal frequency code;e) locating the cells in a next row of the matrix that is not assignedone of the chip; f) locating the columns of the located cells that arenot assigned the same chip; g) locating the column with the least numberof chips; h) assigning the chip to the cell in the column with the leastnumber of chips when a column is located; i) locating the column withthe second least number of chips when the column with a least number ofchips is not located; j) assigning the chip to the cell in the columnwith the second least number of chips when the next column is located;k) returning the one of the error message or the invalid code set whenno next column is located; l) determining if the chip is the last chip;m) repeating steps d through l when the chip is not the last chip; n)determining if the next orthogonal frequency code is the last orthogonalfrequency code; o) repeating steps c through n when the next orthogonalfrequency code is not the last orthogonal frequency code; and p)returning the completed matrix when the last chip in the last code hasbeen assigned a location.
 10. The method of claim 1 further comprisingthe step of: setting an orthogonal frequency coding multi-tag systembandwidth having a system center frequency.
 11. An asynchronous passivemulti-tag system for detecting each one of plural surface acoustic waveorthogonal frequency coded devices in a multi-tag system, the systemcomprising: an orthogonal frequency coding system bandwidth having asystem center frequency; plural surface acoustic wave devices eachproducing a different orthogonal frequency coded signal having the samenumber of chips in the code, each of the different OFC signals includinga chip offset time delay; an algorithm for assigning an orthogonalfrequency coded identification to each of the plural devices; and atransceiver in communication with the plural surface acoustic wavedevice for transmitting an orthogonal interrogation signal to the pluralsurface acoustic wave devices and receiving the different orthogonalcoded signals from said plural surface acoustic wave devices.
 12. Thesurface acoustic wave device of claim 11, wherein the chip offset delaycomprises: a one chip offset delay between all of the plural orthogonalfrequency codes in the system.
 13. The surface acoustic wave device ofclaim 11, wherein the chip offset delay comprises: a two chip offsetdelay between all of the plural orthogonal frequency codes in thesystem.
 14. The system of claim 11 wherein the algorithm comprises: afirst set of instructions to determine a M by N code matrix dimensionbased on the number of orthogonal frequency codes needed M and thenumber of locations chips can populate N, each row corresponding to onesurface acoustic wave device orthogonal frequency code and each cell ineach row corresponding to one orthogonal chip and the chips areorthogonal to each other at their respective center frequencies; and asecond set of instructions to populate each cell of the matrix with oneof the orthogonal frequency chips with a different one of the orthogonalfrequencies in each cell in each column.
 15. A surface acoustic wavedevice comprising: a substrate having a banks of reflectors and atransducer and antenna pair coupled with the banks of reflectorsfabricated on the substrate for producing plural stepped frequencies asan orthogonal coded signal with a chip offset delay to increase codediversity, each stepped frequency having a different center frequencywithin a bandwidth.
 16. The surface acoustic wave device of claim 15,wherein the chip offset delay comprises: one single zero weightreflector grating for a one chip offset delay to increase codediversity.
 17. The surface acoustic wave device of claim 15, wherein thechip offset delay comprises: two or more zero weight reflector gratingsfor at least two chip offset delays to increase code diversity.
 18. Thesurface acoustic wave device of claim 15, wherein the chip offset delaycomprises: a zero weight reflector grating between each one of theplural reflectors to produce the orthogonal frequency code signal with achip delay between each one of the plural orthogonal frequencies toincrease code diversity.
 19. The surface acoustic wave device of claim15, wherein the bank of reflector gratings comprise: a variable weightedreflector grating to increase code diversity.
 20. The device of claim 19wherein the variable weighted reflector grating comprise: a spatiallyweighted reflector grating to generate a stopband response.
 21. Thedevice of claim 15 wherein the plural stepped frequencies are contiguousin time.
 22. The device of claim 15 wherein the plural steppedfrequencies are not contiguous in time.